I doubt that there's a definitive date but you can obtain a definitive answer by contacting the Graz tourist office. You can e-mail them: [email protected]
or, for a quicker response, phone them on 00 43 316 80750
Already started in Vienna .Usually around the last week in June before the school holidays. I take it Graz won`t be much different. Mind you, they get earlier every year!